The Surface Velocity Response of a Tropical Glacier to Intra and Inter Annual Forcing, Cordillera Blanca, Peru

remote sensing

Article The Surface Velocity Response of a Tropical Glacier to Intra and Inter Annual Forcing, Cordillera Blanca, Peru

Andrew Kos 1,* , Florian Amann 2, Tazio Strozzi 3 , Julian Osten 2, Florian Wellmann 4 , Mohammadreza Jalali 2 and Anja Dufresne 2

1 Terrasense Switzerland Ltd., 9470 Buchs, Switzerland 2 Department of Engineering Geology and Hydrogeology, RWTH University, 52062 Aachen, Germany; [email protected] (F.A.); [email protected] (J.O.); [email protected] (M.J.); [email protected] (A.D.) 3 Gamma Remote Sensing Ltd., 3073 Gümligen, Switzerland; [email protected] 4 Unit of Computational Geoscience & Reservoir Engineering, RWTH University, 52062 Aachen, Germany; ﬂ[email protected] * Correspondence: [email protected]

Abstract: We used synthetic aperture radar offset tracking to reconstruct a unique record of ice surface velocities for a 3.2 year period (15 January 2017–6 April 2020), for the Palcaraju glacier located above Laguna Palcacocha, Cordillera Blanca, Peru. Correlation and spatial cluster analysis of residuals of linear ﬁts through cumulative velocity time series, revealed that velocity variations were controlled by the intra-annual outer tropical seasonality and inter-annual variation in Sea Surface Temperature Anomalies (SSTA), related to the El Niño Southern Oscillation (ENSO). The seasonal signal was dominant, where it was sensitive to altitude, aspect, and slope. The measured velocity variations are related to the spatial and temporal variability of the glacier’s surface energy and mass Citation: Kos, A.; Amann, F.; Strozzi, T.; Osten, J.; Wellmann, F.; Jalali, M.; balance, meltwater production, and subglacial water pressures. Evaluation of potential ice avalanche Dufresne, A. The Surface Velocity initiation areas, using deviations from linear long-term velocity trends, which were not related to Response of a Tropical Glacier to Intra intra- or inter-annual velocities, showed no evidence of imminent avalanching ice instabilities for the and Inter Annual Forcing, Cordillera observation period. Blanca, Peru. Remote Sens. 2021, 13, 2694. https://doi.org/10.3390/ Keywords: SAR offset tracking; glacier surface velocity; glacier instability; glacier hazards; ice rs13142694 avalanches; ENSO; glacier mass balance; glacier surface energy

Academic Editors: Paolo Mazzanti and Saverio Romeo 1. Introduction Received: 10 June 2021 The Cordillera Blanca (CB) is the most extensively glaciated mountain range in Peru [1] Accepted: 6 July 2021 Published: 8 July 2021 where the present-day climate is characterized by a distinct seasonality, with a dry season from May to September and a wet season from October to April. The seasonality is con-

Publisher’s Note: MDPI stays neutral trolled by the oscillation of the inner-tropic convergence zone [2]. Seasonal temperature with regard to jurisdictional claims in variations are small but vary significantly on a daily basis [2]. Wet season snow accumu- published maps and institutional affil- lation at high elevation and meltwater from glaciers are the main source of water [3] for iations. the arid west coast of Peru during the dry seasons. Over the course of the 20th century, glacier mass has significantly contracted (e.g., [1,4–6]). Glacier volume loss may influence the stability state and dynamics of a glacier, as a result of a change of the thermal regime, stress state at the bed-ice interface, and associated changes in geometry. Numerous studies suggest that variations in glacier velocities are related to subglacial water pressures, which Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. are controlled by seasonal meltwaters or infiltration following heavy rainstorms [7–14]. The This article is an open access article supply of subglacial water is regulated by the extent of Firn coverage [15], as well as the distributed under the terms and characteristics of the subglacial drainage system. Pressurized subglacial water reduces the conditions of the Creative Commons effective normal stress at the bed-ice interface, leading to reduced frictional resistance, and Attribution (CC BY) license (https:// thus sliding rates are enhanced [11,15–17]. Detailed observational changes in a glacier’s creativecommons.org/licenses/by/ dynamics as well as its geometry, provide insights into whether a potentially hazardous 4.0/). glacier may develop a critical stability state, or conversely remain harmless [8].

Remote Sens. 2021, 13, 2694. https://doi.org/10.3390/rs13142694 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, 2694 2 of 18

2. Materials and Methods 2.1. SAR Offset Tracking The calculation of displacement ﬁelds using Synthetic Aperture Radar (SAR) data is possible using offset tracking methods. Offset tracking is normally used for analyzing rapidly moving objects, such as glaciers, because it overcomes the loss of signal, due to decorrelation, when using InSAR techniques over long time intervals [18–21]. As the glaciers in the Cordillera Blanca of Peru are relatively small, offset tracking is only feasible using high-resolution SAR images with a resolution of ~2–3 m. Using a unique, continuous time series of archived TerraSAR-X (TSX) radar imagery for the period 15 January 2017–6 April 2020 (3.2 years) we reconstructed ice surface velocities for the Palcaraju glacier. The dataset consists of 51 TSX radar images that were acquired on a descending orbit with a ground resolution of 3 m (Table1). The radar images were acquired at 10.53 GMT and the distribution of re-visit intervals for the 50 image pairs was 11 days (2 pairs), 22 days (43 pairs), 33 days (1 pair), and 44 days (4 pairs).

Table 1. TSX SAR offset tracking displacement maps time intervals, perpendicular baseline, and resolution.

Scene Image Pair Date Days Perpendicular Baseline Resolution 1 6 April 2020 3 m 2 1 15 March 2020 22 74.4 3 m 3 2 31 January 2020 44 1.5 3 m 4 3 9 January 2020 22 −146.8 3 m 5 4 18 December 2019 22 104.7 3 m 6 5 26 November 2019 22 −112.4 3 m 7 6 24 October 2019 33 −44.6 3 m 8 7 02 October 2019 22 136.4 3 m 9 8 10 September 2019 22 −137.0 3 m 10 9 19 August 2019 22 203.5 3 m 11 10 28 July 2019 22 −125.7 3 m 12 11 14 June 2019 44 46.0 3 m 13 12 23 May 2019 22 −14.1 3 m 14 13 1 May 2019 22 29.9 3 m 15 14 9 April 2019 22 −4.2 3 m 16 15 29 March 2019 11 −103.0 3 m 17 16 07 March 2019 22 6.1 3 m 18 17 13 February 2019 22 −78.5 3 m 19 18 22 January 2019 22 174.7 3 m 20 19 31 December 2018 22 −88.2 3 m 21 20 09 December 2018 22 84.8 3 m 22 21 17 November 2018 22 −25.8 3 m 23 22 26 October 2018 22 71.4 3 m 24 23 4 October 2018 22 −222.0 3 m 25 24 12 September 2018 22 280.1 3 m 26 25 21 August 2018 22 −164.2 3 m 27 26 30 July 2018 22 148.7617 3 m 28 27 8 July 2018 22 26.9 3 m 29 28 16 June 2018 22 −17.8 3 m 30 29 25 May 2018 22 4.0 3 m 31 30 3 May 2018 22 −66.2 3 m 32 31 11 April 2018 22 106.8 3 m 33 32 20 March 2018 22 −220.7 3 m 34 33 26 February 2018 22 −65.0 3 m Remote Sens. 2021, 13, 2694 3 of 18

Table 1. Cont.

Scene Image Pair Date Days Perpendicular Baseline Resolution 35 34 13 January 2018 44 133.6 3 m 36 35 2 January 2018 11 −149.4 3 m 37 36 11 December 2017 22 30.0 3 m 38 37 19 November 2017 22 −74.9 3 m 39 38 28 October 2017 22 169.1 3 m 40 39 14 September 2017 44 −5.5 3 m 41 40 23 August 2017 22 246.2 3 m 42 41 1 August 2017 22 133.1 3 m 43 42 10 July 2017 22 −206.8 3 m 44 43 18 June 2017 22 182.6 3 m 45 44 27 May 2017 22 −90.0 3 m 46 45 5 May 2017 22 −87.2 3 m 47 46 13 April 2017 22 107.1 3 m 48 47 22 March 2017 22 139.4 3 m 49 48 28 February 2017 22 −111.8 3 m 50 49 6 February 2017 22 −297.0 3 m 51 50 15 January 2017 22 291.0 3 m

Utilizing a normalized cross-correlation of the amplitude component of the SAR images, offsets were measured with rectangular windows at a set of positions uniformly distributed over the scene. To obtain an accurate estimate of subpixel precision of the correlation peak, correlation function values were fitted using a biquadratic polynomial surface. The time interval of the image pairs can be adjusted according to the expected maximum displacement over the glaciers from 11 days to several months. Mismatches or errors were filtered by applying a threshold to the correlation coefficient [22], by (1) iteratively discarding spurious matches based on the angle and size of displacement vectors in the surrounding areas, (2) applying a low-pass filter on the resultant displacement fields, and (3) applying a 2–98% cumulative cutoff to remove potentially uncertain velocity values and outliers. Such values cannot be realistically validated and are likely to be artifacts of the radar data processing method. Hence they have no physical meaning. Slant range and azimuth offset displacement fields were geocoded and transformed to 3D displacements along the terrain surface using the Advanced Land Observing Satellite (ALOS) World 3D (AW3D30), Digital Elevation Model (DEM) [23]. TSX images were processed in series with offset-tracking procedures [18–21] to 3D ice surface displacement maps. This involved combining slant-range and azimuth offsets by assuming that flow occurs parallel to the ice surface, as estimated from the DEM. Matching window sizes of 128 × 96 pixels (e.g., 202 m × 192 m) were applied with steps of 16 × 12 pixels (e.g., 25 m × 24 m). The displacement maps in m/a were geocoded to a posting of ca. 60 m. For an estimation of the uncertainties in the ice displacement maps, a precision of 1/10th of a pixel in the offset estimation can be assumed [24,25]. The displacement error of TSX data with pixel sizes in ground-range and azimuth direction of 0.9 m × 2.0 m respectively, and a time interval of 11 days, are thus on the order of 10 m/year. For longer time intervals, the noise level increases, hence, a similar displacement error of about 10 m/year can be assumed for other image pairs. The displacement values were extracted from individual pixels from the spatial displacement maps.

2.2. Satellite Image Analysis Surface features and glacier extent were mapped in a geographic information software system [26] using high-resolution satellite Pléiades imagery (Table2). In addition, we visu- ally inspected Google Earth and ESRI World Atlas imagery (Table2) captured between 1999 and 2020. Aspect and slope were calculated using the AW3D30 DEM, and, together with velocity and elevation data, exported with one data point per pixel for further statistical analyses. Remote Sens. 2021, 13, 2694 4 of 18

Table 2. Satellite imagery analyzed in this study.

Image Capture Date Image Source Resolution (m) Accuracy (m) 3 July 2020 Google Earth 24 February 2020 Pleiades 22 June 2019 Google earth 08 June 2019 Pleiades 24 June 2018 Maxar/DigitalGlobe (WV02) * 0.5 8.47 18 June 2017 Google Earth 30 May 2016 Google Earth 30 May 2016 Pleiades 01 June 2016 DigitalGlobe (WV02) * 0.5 10.2 28 April 2013 Google Earth 28 July 2013 Google Earth 5 May 2012 Google Earth 15 January 1999 Earthstar Geographic (Terracolor) * 15 50 31 December 1985 Google Earth 1 January 1970 Google Earth * as published on https:\livingatlas.argis.com/wayback, accesed on 8 July 2021.

2.3. Statistical Analysis of Time Series The residuals from a linear fit of the glacier surface velocities over the 3.2 year observation period were used to conduct various correlation analyses. The analyses were based on about 1300 measurement points. Data time series with less than 50% completeness were removed from the statistical analysis. For the remaining data, where gaps were evident, a linear interpolation was applied to ensure consistent time intervals. The filtered and interpolated data allowed us to perform spatial and temporal correlation analysis between the residuals, precipitation, and SST. The Pearson correlation coefficient was determined for all correlation analyses. As an independent test, the processed time series were also subjected to a time series analysis, without a prior assumption of correlations with climate or weather data. The entire data processing workflow was performed in Python using standard packages for transformation and optimization. The dominant wavelength was extracted for each time series using a Fourier transformation. From this dominant signal, a fit to the time series was performed with a Levenberg-Marquardt or dogleg algorithm, resulting in a single fitted trigonometric function with an estimate of best-fitting values for amplitude, phase, offset, and period, as well as the covariance matrix. Physically unreasonable outliers were removed based on the following criteria: • Period > 2000 days (beyond the observation time; no periods below Nyquist frequency) • Amplitude <–20 and >20 (beyond the data range) • Phase: no obvious outliers • Offset <–4 and >4 (beyond the data range) In total, 28 data points were excluded based on the above criteria.

2.4. Cluster Analysis of the Time Series We employed a Bayesian unsupervised machine learning approach [27], to extract clusters of similar behavior from our surface displacement variations (i.e., residuals). The primary aim of the employed method was to extract clusters from the data based on feature similarity, with consideration of the spatial conﬁguration in the physical space. This combination is enabled through a combination of a Gaussian Mixture Model (GMM) in feature space with a Hidden Markov Random Field (HMRF) model in physical space. Both models are integrated into a Bayesian model, and MCMC sampling is performed to obtain the posterior distribution of the GMM parameters. Remote Sens. 2021, 13, 2694 5 of 18

The GMM was applied to samples of N data points (image pixels) in M-dimensional feature space to determine a set of multivariate Gaussian distributions (L classes). The distributions were parametrized by their mean, µ, and covariance, Σ for each cluster. As features originate from spatial data sets, the HMRF was then used to consider spatial dependencies of sampling points, with a smoothing coefficient, which parameterized the strength of spatial correlation, independently for each class. The model parameters (µ, Σ, β), as well as the latent field values, were obtained through a Bayesian optimization, iterative sampling process using a Markov Chain Monte Carlo (MCMC) approach, following an initial Expectation-Maximization (EM) step. The final association of sampling points to clusters were obtained from the Maximum a posteri- ori (MAP) distribution. In addition, cluster assignment probabilities were obtained from the MCMC chain and combined using information entropy, to obtain a spatial estimate of uncertainty [28], for the assigned cluster values. The segmentation procedure is described in Wang et al. [27] and has previously been applied to geophysical [29] and arctic sea ice [30] data sets. It is implemented in the open- source Python package bayseg, available on https://github.com/cgre-aachen/bayseg, accessed on 10 June 2021. The clustering workflow is presented in an exemplary form in the supplementary information section (Figure S1a–d).

3. Results 3.1. Spatio-Temporal Distribution of Glacier Velocities We calculated the spatial distribution of average daily surface velocities of the Pal- caraju glacier over 50 measurement intervals (i.e., velocity maps with 1300 pixels per interval), for the 3.2 year observation period. As the spatial distribution of individual velocity maps were similar for all 50 intervals, the velocity distribution shown in Figure1 is an appropriate representation for the observation period. Daily surface velocities averaged over 3.2 years ranged between 0.01 and 0.47 m/day, where both their spatial distribution and magnitude are consistent with results obtained from Sentinel-2 data [31]. The displacement time series, representing the residuals of the linear fit and cumulative surface displacements, for selected points shown in Figure1, are available in the supplementary materials (Figures S2–S10). The resulting surface velocities are a combination of basal sliding as well as creep and ablation of the glacier, which cannot be individually quantified without independent measurements. Such measurements are outside the scope of this study. Values from the literature [13] and field measurements [7,9,32] suggest that the contribution of basal sliding to the total surface velocities varies between 50–90%, and is spatially variable across the glacier bed [32]. Higher mean annual surface velocities are observed in areas with a high frequency of crevassing and or steep glacier topography (>30–40◦) (see zones S2, S4a, S4b, E1, E2, and E3 Figures1a and2). Based on the occurrence of ridgelines and terrain steps in the 30 m DEM, we infer that steep glacier sections directly reflect the underlying topography of the glacier bed. Although the slope gradient in Zone S4a (Figures1a and2) is compara- tively flat (20–35◦), such higher velocity rates can be related to larger ice thickness at this location [9,33]. West exposed slopes (Figure3) typically showed the highest mean annual surface velocities, followed by south and east exposed slopes over the 3.2 year observation period. Surface velocities of south exposed slopes tend to decrease with altitude, while surface velocities of East exposed slopes increase with altitude. West exposed slopes also showed a general increase with altitude, however, the trend is reversed at an elevation range of approximately 5400–5700 m.a.s.l. Remote Sens. 2021, 13, 2694 6 of 18 Remote Sens. 2021, 13, x FOR PEER REVIEW 6 of 19

FigureFigure 1. 1.( a(a)) Spatial Spatial distribution distribution of of mean mean daily daily surface surface velocities velocities with with respect respect to to elevation, elevation, showing show- theing zones the zones and pointand point selections selections used inused this in study this study (for location (for location see insert see map),insert (map),b) Spatial (b) Spatial distribution distribution of contoured mean daily surface velocities on the Palcaraju glacier. Elevation range of zone of contoured mean daily surface velocities on the Palcaraju glacier. Elevation range of zone E1 is E1 is 5’400–6050 m a.s.l, and 5’900–6150 m a.s.l for zone S1. 50400–6050 m a.s.l, and 50900–6150 m a.s.l for zone S1. Higher mean annual surface velocities are observed in areas with a high frequency of crevassing and or steep glacier topography (>30–40°) (see zones S2, S4a, S4b, E1, E2, and E3 Figures 1a and 2). Based on the occurrence of ridgelines and terrain steps in the 30 m DEM, we infer that steep glacier sections directly reflect the underlying topography of the glacier bed. Although the slope gradient in Zone S4a (Figures 1a and 2) is compara- tively flat (20–35°), such higher velocity rates can be related to larger ice thickness at this location [9,33].

Remote Sens. 2021, 13, 2694 7 of 18 Remote Sens. 2021, 13, x FOR PEER REVIEW 7 of 19

Remote Sens. 2021, 13, x FOR PEER REVIEW 8 of 19 FigureFigure 2. 2. GlacierGlacier slope map.map.

West exposed slopes (Figure 3) typically showed the highest mean annual surface velocities, followed by south and east exposed slopes over the 3.2 year observation period. Surface velocities of south exposed slopes tend to decrease with altitude, while surface velocities of East exposed slopes increase with altitude. West exposed slopes also showed a general increase with altitude, however, the trend is reversed at an elevation range of approximately 5400–5700 m.a.s.l. Zones with higher surface velocities for all slope aspects were only found below 5700 m a.s.l., suggesting that the steep hanging glacier in E1 and S1 (Figures 1 and 3) are cold glaciers [34], likely to be frozen to the glacier bed. This is supported by estimates of the cold-temperate transition line at approximately 5500 m a.s.l., elevation in the region [35]. Hence, in these areas, the surface velocity field mainly represents creep deformation within the ice body. Below 5700 m a.s.l., the glacier is likely to be polythermal to temperate (i.e., subglacial liquid water is temporarily present), and therefore the measured surface velocities are likely controlled by creep processes, basal sliding along the ice-bed interface, and an indeterminable error due to ablation (e.g., a shift in the slant range geometry between image acquisitions and consequent projection into DEM predating the radar image acquisition, resulting in an over-estimation of surface velocities).

FigureFigure 3. 3. GlacierGlacier aspect map.map.

3.2. Velocity Variations Linear regression analysis (see methods section) reveals a coefficient of determination R2 > 0.90–0.99 for all cumulative time series (Figure 4), indicating steady surface movements with no obvious acceleration phases within the observation period. Approxi- mately 2.6% of the analyzed time series showed an R2 ranging between 0.90–0.96, however, this is primarily due to under-sampling of the time series where data points were missing (Figure 5).

Remote Sens. 2021, 13, 2694 8 of 18

Zones with higher surface velocities for all slope aspects were only found below 5700 m a.s.l., suggesting that the steep hanging glacier in E1 and S1 (Figures1 and3) are cold glaciers [34], likely to be frozen to the glacier bed. This is supported by estimates of the cold-temperate transition line at approximately 5500 m a.s.l., elevation in the region [35]. Hence, in these areas, the surface velocity ﬁeld mainly represents creep deformation within the ice body. Below 5700 m a.s.l., the glacier is likely to be polythermal to temperate (i.e., subglacial liquid water is temporarily present), and therefore the measured surface velocities are likely controlled by creep processes, basal sliding along the ice-bed interface, and an indeterminable error due to ablation (e.g., a shift in the slant range geometry between image acquisitions and consequent projection into DEM predating the radar image acquisition, resulting in an over-estimation of surface velocities).

3.2. Velocity Variations Linear regression analysis (see methods section) reveals a coefﬁcient of determination R2 > 0.90–0.99 for all cumulative time series (Figure4), indicating steady surface movements with no obvious acceleration phases within the observation period. Approximately 2.6% of Remote Sens. 2021, 13, x FOR PEER REVIEW 2 9 of 19 the analyzed time series showed an R ranging between 0.90–0.96, however, this is primarily due to under-sampling of the time series where data points were missing (Figure5).

FigureFigure 4. Spatial 4. Spatial distribution distribution of ofcoefficient coefﬁcient of of determination determination (R (R2)2 from) from the the linear linear correlation correlation analysis. analysis.

Figure 5. Spatial distribution of sampling completeness.

Extracted residuals of the time series from linear fitting revealed that the residuals of the glacier surface velocities fluctuate around the long-term (3.2 years) linear trend. Spa- tial correlation and cluster analysis of the residuals shows that these variations in surface velocity have a spatial and temporal variability with respect to zones in the central, eastern, and western parts of the glacier, as well as zones above 5900 m a.s.l. (Figure 6).

Remote Sens. 2021, 13, x FOR PEER REVIEW 9 of 19

Remote Sens. 2021, 13, 2694 9 of 18 Figure 4. Spatial distribution of coefficient of determination (R2) from the linear correlation analysis.

FigureFigure 5. Spatial 5. Spatial distribution distribution of samplingsampling completeness. completeness.

ExtractedExtracted residuals residuals of of the the time seriesseries from from linear linear fitting fitting revealed revealed that thethat residuals the residuals of of the theglacier glacier surface surface velocities velocities fluctuatefluctuate around around the the long-term long-term (3.2 years) (3.2 years) linear trend.linear Spatial trend. Spa- tial correlationcorrelation and and cluster cluster analysis analysis of theof the residuals residuals shows shows that that these these variations variations in surface in surface velocity have a spatial and temporal variability with respect to zones in the central, eastern, velocity have a spatial and temporal variability with respect to zones in the central, east- and western parts of the glacier, as well as zones above 5900 m a.s.l. (Figure6). ern, andSurface western energy parts and of the glacier glacier, mass as balance well as models zones (SEMB)above 5900 across m thea.s.l. glaciated (Figure An- 6). des [1,36,37] collectively show that the glacier response has a strong spatial variability due to its sensitivity to regional and local meteorological and topographic factors [2,37,38]. In this connection, the observed spatio-temporal variation in our glacier velocity residuals may be interpreted as being closely linked to meteorological and topographical variables, which in turn influence the variability of the glacier’s surface energy, mass balance, meltwater production, and effective stress states at the glacier bed.

3.3. Spatial Correlation and Cluster Analysis A spatial correlation and cluster analysis following the procedure described in Sec- tions 2.3 and 2.4 were applied to elucidate details of the factors influencing the spatio- temporal velocity patterns in different parts of the glacier (Figure7). It is important to note that this analysis is performed independently of the previous correlation evaluations and is performed directly on the fitted time series as an additional investigation using an unsupervised machine learning algorithm. From these analyses, three clusters, each with a distinct behavior, were identified from the residuals (Figure6b). These clusters may be considered as two end-members; an intra-annual and inter-annual cluster, with a transition cluster between the two (Figure7c), revealing a behavior similar to the results of the correlation analysis (Figure7a,b). RemoteRemote Sens. Sens.2021 2021, 13,, 269413, x FOR PEER REVIEW 10 of 1910 of 18

FigureFigure 6. ( 6.a) (a Cumulative) Cumulative surface surface velocities velocities fr fromom six six representative representative points, points, (b) Residuals (b) Residuals of the linear of the fit lineardisplaying ﬁt displaying an intra- an intra-annualannual (seasonal) (seasonal) pattern, pattern, from from three three representative representative points points above above5500 m 5500a.s.l. m(N a.s.l.o. 143), (No. in the 143), East in (No. the East2442), (No. and 2442),West and (No. 752) of the glacier, (c) Residuals of the linear fit displaying an inter-annual pattern, from three representative points c Westfor (No. the 752)glacier of response the glacier, in the ( ) central, Residuals south- of theexposed linear part ﬁt displayingof the glacier an (Nos. inter-annual 702, 1522, pattern,1574), (d from) meteorological three representative data; points for the glacier response in the central, south-exposed part of the glacier (Nos. 702, 1522, 1574), (d) meteorological data; Temperature T, Humidity H, Precipitation P (Palcacocha weather station, altitude 4607 m.a.s.l., latitude 09◦24009.3211”S, 77◦23007.0258”, Instituto Nacional de Investigación en Glaciares y Ecosistemas de Montaña INAIGEM), and (e) Sea Surface Temperature Anomalies (SSTA) shifted by 3 months (see main text) for the NOAA Niño 3.4 region. Remote Sens. 2021, 13, 2694 11 of 18 Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 19

FigureFigure 7. 7. ((aa)) MapMap of correlation correlation coefficients coefficients between between resi residualsduals of of the the long-term long-term linear linear fit fitthrough through the velocity time series and precipitation, measured from the Palcacocha weather station, altitude 4607 the velocity time series and precipitation, measured from the Palcacocha weather station, altitude m.a.s.l., latitude 09°24’09.3211” S, 77°23’07.0258”, INAIGEM, (b) Map of correlation coefficients be- 4607 m.a.s.l., latitude 09◦24009.3211”S, 77◦23007.0258”, INAIGEM, (b) Map of correlation coefficients tween residuals of the long-term linear fit through the velocity time series and SST, (c) Results of c betweenthe cluster residuals analysis of show the long-term the distribution linear fit of through intra, inter the and velocity transitional time series clusters. and SST, ( ) Results of the cluster analysis show the distribution of intra, inter and transitional clusters.

Remote Sens. 2021, 13, 2694 12 of 18

4. Discussion 4.1. Intra-Annual Dominant Cluster The velocities belonging to the intra-annual cluster are found below 5900 m.a.s.l., on slopes with flat to medium steepness (<35◦). The slopes are typically south-southeast and steeply southwest exposed. On relatively flat southwest and steep southeast exposed glacier slopes, at altitudes above 5900 m.a.s.l., the intra-annual signal weakens and becomes dominated by a pattern characteristic of the inter-annual cluster. This cluster is characterized by glacier surface velocities that are in phase with the outer tropical seasons. The velocities generally peak in the dry season and subsequently reach a minimum in the following wet season (Figure6b). Meteorological data from the region provided by INAIGEM (Palcacocha weather station 4607 m.a.s.l.) show relatively constant mean monthly temperatures and a distinct seasonal fluctuation in monthly precipitation (Figure6d). Statistical analysis of the residuals from this cluster shows an anti-correlation with monthly precipitation. Higher precipitation during the wet season corresponds to lower surface velocities and vice versa. Palcaraju glacier is predominantly located above the Equilibrium Line Altitude (ELA) (i.e., 4850–4950 m.a.s.l.) where precipitation during the wet season falls as snow [38], and a temperature-sensitive increase of the snowline occurs towards the dry season. For a slightly different aspect (e.g., ~20◦), but similar altitude at the Shallap glacier, (i.e., a glacier about 10 km south of the Palcaraju glacier), Gurgiser et al. [38] found surface Albedo up to 80% during the wet season and a significantly reduced Albedo during the dry season. Annual differences in the gross glacier mass balance were solely related to ablation below the ELA, which were driven by net shortwave radiation in both seasons (with stronger surface energy fluxes during the dry season), the temperature- affected altitude of the snow line, and snow quantity in the wet season (i.e., reduced albedo). Above the ELA, the mass balance was primarily sensitive to annual cumulative precipitation. Gurgiser et al. [38] suggested that above 5000 m a.s.l. seasonal fluctuations of surface and subsurface melting may change gradually with time and altitude between the seasons. They associate this with gradual changes in the snow line, precipitation sum and type, snow cover, snow age, albedo conditions, and the net shortwave radiation budget. High ablation rates during the dry season coincide with the shortwave budget and surface/subsurface melting peaks. Thus, our surface velocity variations in the intra-annual cluster correspond with seasonal variations in ice-melt water production, which in turn modifies subglacial pressure conditions and basal motion.

4.2. Inter-Annual Dominant Cluster The inter-annual cluster is characterized by glacier surface velocity variations that are most likely inﬂuenced by factors controlling subglacial water pressure conditions over a longer temporal scale. We compared the Sea Surface Temperature (SST) curve for the Niño 3.4 region (National Oceanic and Atmospheric Administration, NOAA) to the residuals of our surface velocity time series. Similar to Maussion et al. [39] and Francou et al. [40], we shifted the SST time series by three months to account for the time lag in the glacier mass balance response, and only consider 0.4 K ≤ SST ≤ –0.4 K, with duration > 6 months [36]. Figure6e shows the SST curve for the observation period. From January to December 2017 the SST intensity and duration do not qualify as either a La Niña or El Niño event. Between December 2017 and July 2018, the SST intensity and duration qualify this period as a La Niña event, which is followed by an El Niño event commencing in December 2019, extending through to September 2020. The duration of SST > 0.4 K from 20 January, to 15 June 2020, does not qualify as an El Niño event. We note that prior to our observation period, SST was 1.5 K for more than 6 months indicating a strong El Niño event in 2016 (not shown in Figure6e). Remote Sens. 2021, 13, 2694 13 of 18

We find that the observed Sea Surface Temperature Anomalies (SSTA) show a strong correlation (r > 0.5, p < 0.05) with the residuals obtained from surface velocity time series in the inter-annual cluster (Figure6c,e). The general decrease in surface velocities at the beginning of the time series corresponds to insignificant SST variations verging into a La Niña event starting in December 2017. From March 2017, SST increases gradually. This is associated with a gradual increase in surface velocities and corresponds to the subsequent El Niño (December 2019–September 2020). Maussion et al. [39] used an SEB/SMB model calibrated against a 4-year temperature time series obtained on the Shallap glacier. Reanal- ysis of downscaled atmospheric variables were used to estimate the monthly SEB/SMB for the period 1980–2013. Correlation analysis revealed a strong anti-correlation (r < −0.5, p < 0.05) between SSTA and individual fluxes of the SEB/SMB. During an El Niño event, the correlation was attributed to increased air temperatures, leading to an elevated snow- fall line, an increase in short-wave radiation, and reduced precipitation [39]. At higher altitudes, the ENSO correlation was found to be weaker and mostly related to changes in total precipitation. Therefore, during an El Niño event, meltwater production is strongly enhanced, where subglacial water pressure conditions influence glacier surface velocities, concomitant to the approximate duration of the El Niño event. Our results also show that steep slopes with both East and West orientations, as well as relatively flat areas (regardless of altitude), are prone to inter-annual glacier surface velocity changes as a result of ENSO. This is supported by the findings of Kaser and Georges [2], where regional-scale differences in the ELA between E- and W-facing glaciers were observed in the CB. They found a zonal asymmetry caused by convective cloud development in the afternoon, which influences the radiation balance and ablation. In the morning, east exposed slopes received a high amount of shortwave solar radiation, whilst during the day, clouds develop, and west exposed glaciers receive a significantly lower amount of shortwave solar radiation. Further, Gurgiser et al. [38] found a topographic signature in surface energy and mass balance above 5000 m a.s.l at the Shallap glacier, where the combination of aspect and increased slope steepness results in a smaller incidence for solar radiation and a slower decrease in Albedo.

4.3. Implications for Avalanching Glacier Instabilities Based on our continuous time series of surface velocities, and high-resolution satellite imagery we evaluated whether avalanching glacier instabilities were evident on the Palcaraju glacier for our period of observation. Various authors have suggested a high glacier lake outburst flood (GLOF) susceptibility at Laguna Palcacocha due to the potential of avalanching glaciers, that could induce an impulse wave and result in moraine over- topping [41–43]. A GLOF susceptibility approach, such as those of Wang et al. [44] and Bolch et al. [45] were applied by Emmer and Vilimek [46] for Laguna Palcacocha. Those first-order assessments may only be used as a basis for prioritizing more comprehensive hazard assessments at the local scale [44,45], and require region-specific adjustments to the criteria used [46]. Somos-Valenzuela et al. [42], and Frey et al. [41] defined hazard scenarios for modelling the expected hazard cascade at Laguna Palcacocha. The characteristics of the ice avalanche scenarios, for example, volume and area of initiation, were arbitrarily selected, and lack the detailed analysis concerning the glacier state and dynamics, which are required to understand ice avalanche potential. The scenario definition, in terms of volume for the nearby Laguna 513 can be traced back to those reported by Schneider et al. [47]. The ice avalanche scenarios, selected for the Palcacocha GLOF modeling are therefore poorly constrained, and may ultimately lead to a misrepresentation of the GLOF risk (i.e., particularly when considering pessimistic or worst case hazard scenarios). Remote Sens. 2021, 13, 2694 14 of 18

We focus our evaluation of potential areas of ice avalanche initiation by identify- ing deviations from the linear long-term velocity trends that are not related to intra or inter-annual velocities (e.g., indications for an imminent glacier instability), as well as qualitative features of the glacier from high-resolution satellite imagery. The evaluation of ice avalanching potential is primarily concerned with the characteristics of the (thermal) contact between a glacier and the bedrock [48–50] as well as the type of starting zones rec- ognized as being important for their initiation [49]. Type I starting zones have a relatively large area of bedrock with an almost constant slope, where glacier stability depends upon altitude [48,49], and the proportion of the glacier frozen to the bedrock [50]. Failure of cold glaciers (Type IA), which are those that are frozen to the glacier bed, are primarily controlled by intra-glacial rupture processes, and typically occur on bedrock inclinations > 45◦ [8,50,51]. Detachment in steep, cold glaciers is associated with crevasse formation and accelerating surface velocities. For polythermal or temperate glaciers (Type IB), the bedrock inclination for starting zones are >25◦, where several factors, such as adhesion to the glacier bed, proportion of glacier frozen to the bed, lateral support, and subglacial water pressure influence glacier stability [8,49,50]. Type II starting zones are associated with abrupt changes in bedrock inclination [49], where glaciers may develop a steep cliff, and unstable ice slabs form parallel to the cliff. At the Palcaraju glacier, Type IA starting zones are expected to occur at altitudes above ~5500 m a.s.l. with a slope angle > 45◦. On the Palcaraju glacier, those areas include: (1) the South face of the Palcaraju summit, which is a hanging glacier suggested as a potential ice avalanche scenario by Vilimek et al. [43] (Figure1, zone S1), (2) the upper part of the steep glaciated ridge in zone S2 (Figure1), and (3) the hanging glaciers on the SW-slope of the Pucaranra West face (Figure1, zone E1). At these locations, satellite imagery indicates evidence for relatively small snow avalanches and/or ice falls, some of which reach the relatively flat glacier area above ~5200 m a.s.l. The time series of surface velocities from these locations all show a linear trend (R2 > 0.97), and the scale of acceleration/deceleration phases of the glacier correspond to seasonal dominated oscillations in S2 and inter-annual dominated oscillations in zone S1 and E2. The steep (up to 50◦) glaciated ridge between 5200 and 5750 m a.s.l. in zones S2, show mean daily surface velocities of >0.3 m/d. Mean surface velocities of 0.2–0.3 m/d are solely found above 5500 m (Figure1). Below 5 0500 m a.s.l., where the glacier is likely to be polythermal to temperate, daily surface velocities decrease to >0.2 m/d. All velocity time series in this region exhibit a linear trend (R2 > 0.98), and acceleration/deceleration phases are associated with seasonal-scale dominated oscillations. The potential ice avalanche release area suggested by Frey et al. [41], is located 200–300 m east of the steep ridge, on a 25–30◦ inclined terrace, at approximately 5430 to 5525 m a.s.l. (Figure1, zone S3). Satellite imagery shows that the ice thickness and area located on this terrace reduced significantly between 2013 and 2020 (Figure8). The remaining glacier ice at this location shows mean surface velocities < 0.1 m/d with seasonal dominated oscillation in the West and inter-annual dominated oscillation in the East (Figure S1). Below ~5400 m a.s.l., the slope of the glacier surface ranges between 1◦–35◦ with some steeper sections in the Northwest and Southeast. For zone S4a (Figure1), where higher surface velocities are observed (i.e., >0.3 m/d), the slope parallel to the glacier flow lines range between 20–35◦ (<30◦ on average). As mentioned earlier, this zone is characterized by an elevated ice thickness and hence elevated velocities [9,33]. The surface velocity trends over the observation period are linear (R2 > 0.99), and acceleration/deceleration phases correspond to inter-annual scale-dominated oscillations (Figure S2). The two zones showing higher velocities in the eastern part of the glacier (E2 and lower part of zone E1 in Figure1) are likely associated with terrain steps in the glacier bed and multiple crevasses perpendicular to the glacier flow line. The maximum average velocity is 0.2–0.4 m/d. Below the higher velocity zones, the average daily velocity decreases to < 0.2 m/d. Linear Remote Sens. 2021, 13, 2694 15 of 18

Remote Sens. 2021, 13, x FOR PEER REVIEWregression analysis shows a linear velocity trend (E1 R2 > 0.97, E2 R2 > 0.98),16 again, of 19

characterized by a strong seasonal-scale oscillation (Figures S3 and S4).

FigureFigure 8.8.Satellite Satellite imageimage ofof ZoneZone S3S3 onon ((aa)) 2020 AugustAugust 2013 2013 and and ( b(b)) 3 3 July July 2020 2020 (Google (Google Earth). Earth).

Somos-ValenzuelaBelow ~5400 m a.s.l., et al.the [42 slope] suggested of the glacie a potentialr surface ice ranges avalanche between starting 1°–35° zone with at 5some0202 m.a.s.l.steeper insections zone S5in (Figurethe Northwest1), located and at Southe the toeast. of For a steep zone glaciatedS4a (Figure flank. 1), where Within higher the areasurface delineated velocities by are Somos-Valenzuela observed (i.e., >0.3 et al.m/d) [42, ],the the slope slope parallel of the to glacier the glacier varies flow between lines 10–30range◦ .between Satellite 20–35° imagery (<30° shows on thataverage). the lower As ment endioned of this earlier, zone is this in close zone contact is characterized with the surroundingby an elevated glacier ice withoutthickness any and visible hence terrain elevat step,ed velocities which renders [9,33]. anyThe locally surface enhanced velocity processtrends over kinematically the observation unlikely. period Further, are thelinear surface (R2 > velocities0.99), and are acceleration/deceleration between 0.1–0.2 m/d, exhibitingphases correspond a linear trend to inter-annual (R2 > 0.97) scale-dominated with acceleration/deceleration oscillations (Figure phases S2). corresponding The two zones toshowing distinct higher seasonal velocities dominated in the oscillations eastern part (Figure of the S5). glacier (E2 and lower part of zone E1 in FigureDespite 1) are all accumulatedlikely associated surface with velocity terrain timesteps seriesin the exhibitingglacier bed linear and multiple trends (e.g., cre- Rvasses2 > 0.95), perpendicular potential instabilities to the glacier may formflow atline. the The glacier maximum terminus, average which velocity are characterized is 0.2–0.4 bym/d. glacier Below flow the directionshigher velocity perpendicular zones, the to average steep terraindaily velocity steps (Type decreases IB or to Type < 0.2 II m/d. ice avalancheLinear regression starting zones).analysis The shows velocity-time a linear velocity series fortrend the (E1 glacier R2 > terminus 0.97, E2 R did2 > not0.98), suggest again, thecharacterized development by a of strong significant seasonal-scale ice instabilities oscillation within (Figures the observation S3 and S4). period. However, Somos-Valenzuela et al. [42] suggested a potential ice avalanche starting zone at 5’202 m.a.s.l. in zone S5 (Figure 1), located at the toe of a steep glaciated flank. Within the area delineated by Somos-Valenzuela et al. [42], the slope of the glacier varies between 10–30°.

Remote Sens. 2021, 13, 2694 16 of 18

as our surface velocity ﬁeld has a 60 m spatial resolution, instabilities smaller than the resolution may not be clearly detectable. Satellite images obtained from 2012 and 2020 show that two distinct zones at the terminus exhibit frequent ice falls or snow avalanches. One zone is located at the terminus of zone S4a and on the terminus of E3 (Figure1). Due to the dynamics of the glacier, small icefall events at these locations are expected. Those types of events may occasionally reach the Laguna, causing small-scale disturbances, an example of which was captured by cameras operated by INAIGEM (e.g., small icefall on 5 February 2019 and a snow avalanche on 17 January 2021). However, based on available data it is not possible to ascertain whether they are single or multiple icefall events. Evaluation of ice avalanche potential for the Palcaraju glacier, based on our velocity time series indicates that an imminent failure of a glacier instability was not evident during the observation period. However, continuous observations, for which our study provides an important baseline, would be necessary to assess whether the behavior of the glacier changes over time, and to detect indications for an imminent ice avalanche.

Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/rs13142694/s1, Figures S1–S10 Conceptual representation of the clustering approach and displacement time series residuals for selected points. Author Contributions: Conceptualization, A.K. and F.A.; methodology, A.K., F.A., F.W. and M.J.; software, T.S. and J.O.; investigation, A.K., F.A., A.D., F.W., M.J. and T.S.; data curation, J.O.; writing— original draft preparation, A.K. and F.A.; writing—review and editing, A.K., F.A. T.S., J.O., F.W. M.J. and A.D.; visualization, F.W., M.J., and J.O. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Acknowledgments: The TerraSAR-X data are copyrighted by the German Aerospace Center (DLR) and were provided through a commercial data purchase. Permission to use the results for this publication was granted by the firm RWE AG. We acknowledge the detailed review and sugges- tions provided by Martin Funk, VAW ETH Zurich. We thank two anonymous reviewers for their improvements to the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

References 1. Vuille, M.; Francou, B.; Wagnon, P.; Juen, I.; Kaser, G.; Mark, B.G.; Bradley, R.S. Climate change and tropical Andean glaciers: Past, present and future. Earth-Sci. Rev. 2008, 89, 79–96. [CrossRef] 2. Kaser, G.; Georges, C. Changes of the equilibrium-line altitude in the tropical Cordillera Blanca, Peru, 1930–1950, and their spatial variations. Ann. Glaciol. 1997, 24, 344–349. [CrossRef] 3. Gascoin, S.; Kinnard, C.; Ponce, R.; Lhermitte, S.; MacDonell, S.; Rabatel, A. Glacier contribution to streamflow in two headwaters of the Huasco River, Dry Andes of Chile. Cryosphere 2011, 5, 1099–1113. [CrossRef] 4. Bolch, T.; Kulkarni, A.; Kääb, A.; Huggel, C.; Paul, F.; Cogley, J.G.; Frey, H.; Kargel, J.S.; Fujita, K.; Scheel, M.; et al. The state and fate of Himalayan glaciers. Science 2012, 336, 310–314. [CrossRef] 5. Georges, C. 20th-Century Glacier Fluctuations in the Tropical Cordillera Blanca, Perú. Arctic, Antarct. Alp. Res. 2004, 36, 100–107. [CrossRef] 6. Kaser, G.; Ames, A.; Zamora, M. Glacier Fluctuations and Climate in the Cordillera Blanca, Peru. Ann. Glaciol. 1990, 14, 136–140. [CrossRef] 7. Hooke, R.L.; Pohjola, V.A.; Jansson, P.; Kohler, J. Intra-seasonal changes in deformation profiles revealed by borehole studies, Storglaciären, Sweden. J. Glaciol. 1992, 38, 348–358. [CrossRef] 8. Faillettaz, J.; Funk, M.; Vincent, C. Avalanching glacier instabilities: Review on processes and early warning perspectives. Rev. Geophys. 2015, 53, 203–224. [CrossRef] 9. Vincent, C.; Morceau, L.U. Sliding velocity fluctuations and subglacial hydrology over the last two decades on Argentière glacier, Mont Blanc area. J. Glaciol. 2016, 62, 805–815. [CrossRef] 10. Iken, A.; Bindschadler, R.A. Combined measurements of Subglacial Water Pressure and Surface Velocity of Findelengletscher, Switzerland: Conclusions about Drainage System and Sliding Mechanism. J. Glaciol. 1986, 32, 101–119. [CrossRef] Remote Sens. 2021, 13, 2694 17 of 18

11. Bindschadler, R. The Importance of Pressurized Subglacial Water in Separation and Sliding at the Glacier Bed. J. Glaciol. 1983, 29, 3–19. [CrossRef] 12. Engelhardt, H.F. Water in glaciers: Observations and theory of the behaviour of water levels in boreholes. Z. Gletsch. Glaziologie 1978, 14, 35–60. 13. Weertman, J. The Theory of Glacier Sliding. J. Glaciol. 1964, 5, 287–303. [CrossRef] 14. Agassiz, L. Système Glaciaire, ou Recherches sur les Glaciers: Pt. 1. Novelles Études et Expériences sur les Glaciers Actuels. Mason, V., Ed.; 1847. Available online: http://www.google.cat/books?id=MdQWAAAAQAAJ&printsec=frontcover&vq=froid&hl=ca& output=html_text&source=gbs_ge_summary_r&cad=0 (accessed on 10 June 2021). 15. Fountain, A.G.; Walder, J.S. Water ﬂow through temperate glaciers. Rev. Geophys. 1998, 36, 299–328. [CrossRef] 16. Kääb, A.; Jacquemart, M.; Gilbert, A.; Leinss, S.; Girod, L.; Huggel, C.; Falaschi, D.; Ugalde, F.; Petrakov, D.; Chernomorets, S.; et al. Sudden large-volume detachments of low-angle mountain glaciers–more frequent than thought? Cryosphere 2021, 15, 1751–1785. [CrossRef] 17. Harper, J.T.; Humphrey, N.; Pfeffer, W.T.; Lazar, B. Two modes of accelerated glacier sliding related to water. Geophys. Res. Lett. 2007, 34.[CrossRef] 18. Paul, F.; Bolch, T.; Kääb, A.; Nagler, T.; Nuth, C.; Scharrer, K.; Shepherd, A.; Strozzi, T.; Ticconi, F.; Bhambri, R.; et al. The glaciers climate change initiative: Methods for creating glacier area, elevation change and velocity products. Remote Sens. Environ. 2015, 162, 408–426. [CrossRef] 19. Werner, C.; Wegmuller, U.; Strozzi, T.; Wiesmann, A. Precision estimation of local offsets between pairs of SAR SLCs and detected SAR images. In Proceedings of the 2005 IEEE International Geoscience and Remote Sensing Symposium, Seoul, Korea, 25–29 July 2005; pp. 4803–4805, ISBN 0-7803-9050-4. 20. Strozzi, T.; Luckman, A.; Murray, T.; Wegmuller, U.; Werner, C.L. Glacier motion estimation using SAR offset-tracking procedures. IEEE Trans. Geosci. Remote Sens. 2002, 40, 2384–2391. [CrossRef] 21. Gray, A.L.; Mattar, K.E.; Vachon, P.W.; Bindschadler, R.; Jezek, K.C.; Forster, R.; Crawford, J.P. InSAR results from the RADARSAT Antarctic Mapping Mission data: Estimation of glacier motion using a simple registration procedure. In Proceedings of the IGARSS ‘98, Sensing and Managing the Environment, IEEE International Geoscience and Remote Sensing, Symposium, Seattle, WA, USA, 6–10 July 1998; Volume 3, pp. 1638–1640, ISBN 0-7803-4403-0. 22. Friedl, P.; Seehaus, T.; Braun, M. Global time series and temporal mosaics of glacier surface velocities, derived from Sentinel-1 data. Earth Syst. Sci. Data Discuss. 2021. in review. 23. Mohr, J.J.; Reeh, N.; Madsen, S.N. Three-dimensional glacial ﬂow and surface elevation measured with radar interferometry. Nature 1998, 391, 273–276. [CrossRef] 24. Strozzi, T.; Paul, F.; Wiesmann, A.; Schellenberger, T.; Kääb, A. Circum-Arctic Changes in the Flow of Glaciers and Ice Caps from Satellite SAR Data between the 1990s and 2017. Remote Sens. 2017, 9, 947. [CrossRef] 25. Paul, F.; Bolch, T.; Briggs, K.; Kääb, A.; McMillan, M.; McNabb, R.; Nagler, T.; Nuth, C.; Rastner, P.; Strozzi, T.; et al. Error sources and guidelines for quality assessment of glacier area, elevation change, and velocity products derived from satellite data in the Glaciers_cci project. Remote Sens. Environ. 2017, 203, 256–275. [CrossRef] 26. Pellikka, P.K.E.; Rees, G. Remote Sensing of Glaciers: Techniques for Topographic, Spatial and Thematic Mapping of Glaciers; CRC Press: Boca Raton, FL, USA, 2010; ISBN 9780367384647. 27. Wang, H.; Wellmann, J.F.; Li, Z.; Wang, X.; Liang, R.Y. A Segmentation Approach for Stochastic Geological Modeling Using Hidden Markov Random Fields. Math. Geol. 2017, 49, 145–177. [CrossRef] 28. Wellmann, J.F.; Regenauer-Lieb, K. Uncertainties have a meaning: Information entropy as a quality measure for 3-D geological models. Tectonophysics 2012, 526–529, 207–216. [CrossRef] 29. Wang, H.; Wellmann, F.; Zhang, T.; Schaaf, A.; Kanig, R.M.; Verweij, E.; Hebel, C.; Kruk, J. Pattern Extraction of Topsoil and Subsoil Heterogeneity and Soil-Crop Interaction Using Unsupervised Bayesian Machine Learning: An Application to Satellite-Derived NDVI Time Series and Electromagnetic Induction Measurements. J. Geophys. Res. Biogeosci. 2019, 124, 1524–1544. [CrossRef] 30. Herbert, C.; Camps, A.; Wellmann, F.; Vall-Llossera, M. Bayesian Unsupervised Machine Learning Approach to Segment Arctic Sea Ice Using SMOS Data. Geophys. Res. Lett. 2021, 48, e2020GL091285. [CrossRef] 31. Millan, R.; Mouginot, J.; Rabatel, A.; Jeong, S.; Cusicanqui, D.; Derkacheva, A.; Chekki, M. Mapping Surface Flow Velocity of Glaciers at Regional Scale Using a Multiple Sensors Approach. Remote Sens. 2019, 11, 2498. [CrossRef] 32. Blake, W.; Fischer, U.H.; Bentley, C.R.; Clarke, G.K.G. Instruments and Methods: Direct measurement of sliding at the glacier bed. J. Glaciol. 1994, 40, 595–599. [CrossRef] 33. Cuffey, K.M.; Paterson, W.S.B. The physics of Glaciers, 4th ed.; Elsevier: Amsterdam, The Netherlands, 2010; ISBN 978-0-123-69461-4. 34. Pralong, A.; Funk, M. On the instability of avalanching glaciers. J. Glaciol. 2006, 52, 31–48. [CrossRef] 35. Vimeux, F.; Ginot, P.; Schwikowski, M.; Vuille, M.; Hoffmann, G.; Thompson, L.G.; Schotterer, U. Climate variability during the last 1000 years inferred from Andean ice cores: A review of methodology and recent results. Palaeogeogr. Palaeoclim. Palaeoecol. 2009, 281, 229–241. [CrossRef] 36. Favier, V. One-year measurements of surface heat budget on the ablation zone of Antizana Glacier 15, Ecuadorian Andes. J. Geophys. Res. 2004, 109, 1–15. [CrossRef] 37. Sagredo, E.A.; Rupper, S.; Lowell, T.V. Sensitivities of the equilibrium line altitude to temperature and precipitation changes along the Andes. Quat. Res. 2014, 81, 355–366. [CrossRef] Remote Sens. 2021, 13, 2694 18 of 18

38. Gurgiser, W.; Marzeion, B.; Nicholson, L.; Ortner, M.; Kaser, G. Modeling energy and mass balance of Shallap Glacier, Peru. Cryosphere 2013, 7, 1787–1802. [CrossRef] 39. Maussion, F.; Gurgiser, W.; Großhauser, M.; Kaser, G.; Marzeion, B. ENSO influence on surface energy and mass balance at Shallap Glacier, Cordillera Blanca, Peru. Cryosphere 2015, 9, 1663–1683. [CrossRef] 40. Francou, B. New evidence for an ENSO impact on low-latitude glaciers: Antizana 15, Andes of Ecuador, 0◦280S. J. Geophys. Res. 2004, 109, 1–17. [CrossRef] 41. Frey, H.; Huggel, C.; Chisolm, R.E.; Baer, P.; McArdell, B.; Cochachin, A.; Portocarrero, C. Multi-Source Glacial Lake Outburst Flood Hazard Assessment and Mapping for Huaraz, Cordillera Blanca, Peru. Front. Earth Sci. 2018, 6, 1–16. [CrossRef] 42. Somos-Valenzuela, M.A.; Chisolm, R.E.; Rivas, D.S.; Portocarrero, C.; McKinney, D.C. Modeling a glacial lake outburst flood process chain: The case of Lake Palcacocha and Huaraz, Peru. Hydrol. Earth Syst. Sci. 2016, 20, 2519–2543. [CrossRef] 43. Vilímek, V.; Zapata, M.L.; Klimeš, J.; Patzelt, Z.; Santillán, N. Influence of glacial retreat on natural hazards of the Palcacocha Lake area, Peru. Landslides 2005, 2, 107–115. [CrossRef] 44. Wang, W.; Yao, T.; Gao, Y.; Yang, X.; Kattel, D.B. A First-order Method to Identify Potentially Dangerous Glacial Lakes in a Region of the Southeastern Tibetan Plateau. Mt. Res. Dev. 2011, 31, 122. [CrossRef] 45. Bolch, T.; Peters, J.; Yegorov, A.; Pradhan, B.; Buchroithner, M.; Blagoveshchensky, V. Identification of potentially dangerous glacial lakes in the northern Tien Shan. Nat. Hazards 2011, 59, 1691–1714. [CrossRef] 46. Emmer, A.; Vilímek, V. Review Article: Lake and breach hazard assessment for moraine-dammed lakes: An example from the Cordillera Blanca (Peru). Nat. Hazards Earth Syst. Sci. 2013, 13, 1551–1565. [CrossRef] 47. Schneider, D.; Huggel, C.; Cochachin, A.; Guillén, S.; García, J. Mapping hazards from glacier lake outburst floods based on modelling of process cascades at Lake 513, Carhuaz, Peru. Adv. Geosci. 2014, 35, 145–155. [CrossRef] 48. Huggel, C.; Haeberli, W.; Kääb, A.; Bieri, D.; Richardson, S. An assessment procedure for glacial hazards in the Swiss Alps. Can. Geotech. J. 2004, 41, 1068–1083. [CrossRef] 49. Alean, J. Ice Avalanches: Some Empirical Information about their Formation and Reach. J. Glaciol. 1985, 31, 324–333. [CrossRef] 50. Röthlisberger, H. (Translated from German) Ice Avalanches and Outburst Floods of Glacial Lakes: Offprint, Yearbook of the Swiss Natural Research Society, Scientific Section; 1978. 51. Alean, J. (Translated from German) Studies on the Conditions of Formation and Range of Ice Avalanches. Communications of the Laboratory of Hydraulics. Hydrology and Glaciology; ETH Zurich, 1984; Volume 74.